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Hydrodynamic Dispersion During Infiltration of Water into Soil¹

ABSTRACT

The analysis of hydrodynamic dispersion during one-dimensional sorption of water by soil (horizontal flow) is extended to include the gravitational effects present during one-dimensional infiltration (vertical flow). A power series form for the solution is developed in a manner similar to that developed by Philip for water movement during infiltration. Similar to the sorption analysis, the longitudinal dispersion coefficient was assumed to be a function of water content only. A computer simulation program using CSMP was used to solve the associated differential equations. A single program was found to be suitable as long as the Boltzman parameter (distance divided by the square root of time) was used as the independent variable throughout. An algorithm was developed to give successively better solutions of the soil water diffusion and hydrodynamic dispersion equations.

Infiltration experiments were carried out on a clay loam soil. Both the water and chloride content profiles preserved similarity in terms of the Boltzman parameter. Water and solute coefficients of the power series solutions were calculated from horizontal infiltration and hydraulic conductivity data and used to predict both the water and solute profiles during vertical infiltration. Good agreement between the vertical infiltration data and the theoretical predictions was obtained.

¹ Contribution from Department of Land Resource Science, University of Guelph, Guelph, Ontario, Canada. The authors acknowledge support from the National Research Council of Canada and the Ontario Ministry of Agriculture and Food.

² Professor, Graduate Student and Professional Associate, respectively.

Received for publication December 19, 1977. Accepted for publication May 23, 1979.